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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
Experience with PJM Market Operation, System
Design, and Implementation
Andrew L. Ott
Invited Paper
Abstract—This paper outlines the fundamental features of the
PJM day-ahead energy market and real-time energy market. The
Day-ahead market is based on a voluntary least-cost security constrained unit commitment and dispatch with several fundamental
design features that ensure the market is robust and competitive.
This market offers market participants the option to lock in energy
and transportation charges at binding day-ahead prices. The flexibility of the day-ahead market rules provide all participants with
equal access to the day-ahead market through consistent price signals and by providing all participants with the ability to submit
virtual demand bids and virtual supply offers. These mechanisms
promote liquidity in the markets. Economic incentives drive the
convergence of the day-ahead and real-time market prices. The
real-time energy market is based on security-constrained economic
dispatch and is cleared based on the actual system operating conditions. The LMP-based markets support reliable grid operations
through efficient price signals.
The balancing market is the real-time energy market in which
the clearing prices are calculated every 5 min based on the
actual system operations security-constrained economic dispatch. Separate accounting settlements are performed for each
market, the day-ahead market settlement is based on scheduled
hourly quantities and on day-ahead hourly prices, the balancing
settlement is based on hourly integrated quantity deviations
from day-ahead scheduled quantities and on real-time prices
integrated over the hour. The day-ahead price calculations and
the balancing (real-time) price calculations are based on the
concept of locational marginal pricing (LMP).
Index Terms—Electricity market, locational marginal pricing.
The day-ahead market provides market participants with the
ability to purchase and sell energy at binding day-ahead prices.
It also allows transmission customers to schedule bilateral transactions at binding day-ahead congestion charges based on the
differences in Locational Marginal Prices between the transaction source and sink locations. Load serving entities (LSEs) may
submit hourly demand schedules, including any price sensitive
demand, for the amount of demand that they wish to lock-in
at day-ahead prices. Any generator that has entered into an installed capacity contract must submit an offer schedule into the
day-ahead market even if it is self-scheduled or unavailable due
to outage. Other generators have the option to offer into the dayahead market or into the real-time market. Transmission customers may submit fixed, dispatchable or “up to” congestion bid
bilateral transaction schedules into the day-ahead market and
may specify whether they are willing to pay congestion charges
or wish to be curtailed if congestion occurs in the real-time
market. All spot purchases and sales in the day-ahead market
are settled at the day-ahead prices.
After the day-ahead market bid period closes, PJM calculates
the day-ahead schedule based on the bids, offers, and schedules
submitted based on least-cost, security constrained unit commitment, and dispatch for each hour of the next operating day.
The day-ahead market clearing process incorporates PJM reliability requirements and reserve obligations into the analysis.
The resulting day-ahead hourly schedules and day-ahead LMPs
represent binding financial commitments to the market participants. Financial transmission rights (FTRs) are settled at the
day-ahead LMP values.
I. INTRODUCTION
P
JM OPERATES the world’s largest competitive wholesale
electricity market and one of North America’s largest
power grids. PJM currently coordinates a pooled generating
capacity of more than 67 000 MW and operates a wholesale
electricity market with more than 200 market buyers, sellers
and traders of electricity. The PJM market covers all or parts of
PA, NJ, MD, DE, OH, VA, WV, and the District of Columbia.
With the April 1, 2002, addition of PJM West, for the first
time nationally two separate control areas now operate under
a single energy market, single security-constrained economic
dispatch and a single governance structure across multiple
North American Electric Reliability Councils.
The PJM energy market consists of two markets—a
day-ahead market and a real-time balancing market. The
day-ahead market is a forward market in which hourly clearing
prices are calculated for each hour of the next operating
day based on generation offers, demand bids, virtual supply
offers, virtual demand bids and bilateral transaction schedules
submitted into the day-ahead market. The day-ahead energy
market is a voluntary bid-based market that is cleared using a
security-constrained unit commitment and economic dispatch.
Manuscript received November 26, 2002.
The author is with PJM Interconnection LLC, Norristown, PA 19403-2497
USA.
Digital Object Identifier 10.1109/TPWRS.2003.810698
II. DAY-AHEAD ENERGY MARKET
0885-8950/03$17.00 © 2003 IEEE
OTT: EXPERIENCE WITH PJM MARKET OPERATION, SYSTEM DESIGN, AND IMPLEMENTATION
A. Market Design Objectives
As stated previously, the PJM market design is based on the
concept of LMP. A key feature of an LMP model is that there is a
fundamental consistency between the energy price and the price
of delivery on the transmission system. In this model, the energy
price difference between the injection point and the withdrawal
point is equal to the transmission congestion cost.1 Therefore, a
market participant who injects (sells) energy at location A and
withdraws (purchases) at location B will pay exactly the same
as a market participant who pays the transmission congestion
charge to deliver a bilateral contract from A to B. This consistency is a feature of both the PJM day-ahead market and the
PJM real-time market.
In addition to the LMP concept, the fundamental design objectives of the PJM day-ahead energy market are: 1) to provide
a mechanism in which all participants have the opportunity to
lock in day-ahead financial schedules for energy and transmission; 2) to coordinate the day-ahead financial schedules with
system reliability requirements; 3) to provide incentive for resources and demand to submit day-ahead schedules; and 4) to
provide incentive for resources to follow real-time dispatch instructions.
The first market design objective is accomplished by providing a variety of alternatives for participation in the day-ahead
market. The participation options include the ability to selfschedule resources, the ability to submit bilateral schedules and
the ability to submit offers to sell or bids to buy from the dayahead spot market. This flexibility ensures that all market participants have equal access to the day-ahead market. Therefore,
any barriers to trade in the day-ahead market are minimized so
that the market will be as competitive as possible. In order to
further promote liquidity, the market design also includes the
ability to submit purely financial positions in the form of virtual supply offers and virtual demand bids. In this way, the dayahead market provides both the ability the hedge physical delivery and the ability to enter financial positions into the market.
All positions that are cleared in the day-ahead market are financially binding and will liquidate in the balancing market if they
are not covered by a real-time energy delivery.
The second market design objective is important to ensure
that the day-ahead schedules are physically feasible and
are consistent with reliable system operations. This feature
is significant because it requires that the powerflow model
used to analyze the day-ahead market is consistent with the
powerflow model that is used in real-time system operations.
It also requires that the Day-ahead market is cleared considering the same single contingency criteria and transmission
equipment ratings that are used in real-time operations. Since
the underlying powerflow model and operating constraints
are consistent between the day-ahead forward market and the
real-time dispatch, the LMP signals are consistent between
the day-ahead and real-time markets as well. In addition
to the powerflow model consistency, the day-ahead market
also respects system reserve requirements and the generator
1The current PJM model does not reflect the cost of marginal losses in the
LMP calculation.
529
physical operating limitations.2 This design feature ensures that
the financial schedules that result from the day-ahead forward
market are consistent with the physical transmission capability.
Therefore the day-ahead scheduling process ensures that the
transmission capability is not over-subscribed and ensures that
the generation schedules are consistent with the generator’s
physical capabilities. The fundamental consistency between
the forward market and the real-time market ensures a robust
market design that promotes economic efficiency and it enables
the market to avoid the gaming opportunities that have plagued
other market designs.
The third market design objective involves more than just
the fundamental structure of a two-settlement system.3 It also
requires that there is consistency between the market pricing
mechanisms and that price convergence occurs between the
markets over time.
The following series of examples will illustrate the economic
incentives that exist in the two settlement design.
Example 1: A customer submits a day-ahead demand bid
that clears for 100 MW at an LMP of U.S.$ 20/MWh. In the
real-time market, the customer has 105 MW of demand and the
LMP value is U.S.$ 23/MWh. In this case, the customer’s resulting financial settlement is: day-ahead load payment U.S.$
20/MWh * 100 MW U.S.$ 2000, Real-time balancing payment (105–100) MWh * $23/MWh U.S.$ 115. The total
payment is U.S.$ 2115. If the customer had locked in his total
load of 105 MWh at the Day-ahead price of U.S.$ 20 then his
$2100.4
total payment would have been 105 MWh * $20
Therefore, in this case the customer has the incentive to submit
the actual expected demand into the day-ahead market. This incentive is driven by the fact that the customer experienced a demand increase between the day-ahead and real-time markets at
the same time that the entire market exhibited the same trend as
indicated by the higher real-time LMP.
Example 2: A customer submits a day-ahead demand bid
that clears for 100 MW at an LMP of U.S.$ 20/MWh. In the
real-time market, the customer has 95 MW of demand and the
LMP value is U.S.$ 23/MWh. In this case, the customer’s resulting financial settlement is: day-ahead load payment U.S.$
20/MWh * 100 MW U.S.$ 2000, Real-time balancing pay$115. The total
ment (95–100) MWh * U.S.$ 23/MWh
payment is U.S.$ 1885. If the customer had locked in his total
load of 95 MWh at the Day-ahead price of U.S.$ 20 then his
total payment would have been 95 MWh * $20 U.S.$ 1900.5
Therefore, in this case the customer has the incentive to submit
the lower demand into the day-ahead market. This result demonstrates another feature of the two-settlement system. If a participant takes a position in the opposite direction of the rest of the
2These limitations include the generators startup time, minimum run time,
energy limits, ramp limits, and other physical unit operating constraints.
3The PJM two settlement system consists of a day-ahead financial settlement
and a real-time balancing market.
4This example assumes that the customer’s demand is a small part of the
overall market which means that the small increase in demand would not have
substantially changed the clearing price.
5This example also assumes that the customer’s demand is a small part of the
overall market which means that the small increase in demand would not have
substantially changed the clearing price.
530
market, then economic reward results. This incentive is key to
driving price convergence between the markets.
The incentives illustrated in the examples encourage dayahead market participation because if demand is too low in the
day-ahead market, the customer faces higher real-time prices
and if demand is too high the opposite occurs. In addition, the
desire to obtain forward price certainty and to manage risk also
contribute to the incentive for demand customers to submit dayahead demand bids.
The incentives for generation are best discussed in the context of the fourth design objective. Creating the incentive for resources to follow real-time dispatch instructions is fundamental
to the voluntary bid-based market design. Utilizing a voluntary
market to support reliable grid operations requires strong economic signals that are consistent with real-time reliability requirements of the grid. The best way to illustrate the incentive for generation to follow real-time dispatch instructions is
through the use of additional examples.
Example 3: A generator submits an incremental offer curve
into the day-ahead market for 100 MW at U.S.$ 20 and for 120
MW at U.S.$ 30. The generator offer is cleared in the day-ahead
market for 100 MW at U.S.$ 20. In the real-time market, the generator is requested to increase output by the system operator to
the 120 MW level and the real-time LMP value is U.S.$ 31. The
generator has the incentive to increase its output above the dayahead scheduled amount because the real-time LMP is higher
and the generator will receive the higher real-time price for the
additional megawatt delivered in the real-time market. The generator settlement is: day-ahead 100 MWh * U.S.$ 20/MWh
U.S.$ 2000 and real-time (120–100)MWh * U.S.$ 31/MWh
U.S.$ 620, the total generator revenue is U.S.$ 2620. This
example shows that the generator has incentive to respond to
real-time price increases if the real-time price exceeds the generator’s incremental offer.
Example 4: A generator submits an incremental offer curve
into the day-ahead market for 100 MW at U.S.$ 20 and for 120
MW at U.S.$ 30. The generator offer is cleared in the dayahead market for 120 MW at U.S.$ 45. The next day in the
real-time market, the generator is requested to reduce to 100
MW output and the real-time price falls to U.S.$ 20/MWh because of lower than expected loads. If the generator reduces
output then it must purchase the quantity difference at real-time
price. An examination of the generator’s profit under this scenario will reveal the incentive. The Day-ahead settlement is 120
MWh * U.S.$ 45/MWh U.S.$ 5400, the generators production cost.6 is U.S.$ 2600. If the generator does not reduce output
U.S.$ 2800. If
then its profit is: U.S.$ 5400 U.S.$ 2600
the generator reduces as requested, then the real-time settlement
is: real-time settlement (100–120)MWh * U.S.$ 20 MWh
U.S.$ 400. In this case, the generator’s production cost is reduced to U.S.$ 2000. The generators profit is then equal to U.S.$
5400 U.S.$ 400 U.S.$ 2000 U.S.$ 3000. Therefore, the
generator makes more profit by following the dispatch instruction to reduce output below the day-ahead scheduled level be6This example assumes that the generator submitted an offer equal to its mar-
ginal cost.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
Fig. 1. Day-ahead versus real-time hourly average LMP.
cause the real-time price reduced. Essentially, the incentive is
driven by the fact that the generator was paid a higher price for
the day-ahead scheduled output and was able to buy it back in
the real-time market at the reduced price.
This section has outlined the fundamental design concepts behind the PJM day-ahead market. The next section will examine
market results.
B. PJM Day-Ahead Market Results
The PJM day-ahead energy market was implemented in June
2000. Since the implementation, the convergence between dayahead prices and real-time prices has been narrowing [1]. In the
year 2001, the average day-ahead LMP was U.S.$ 32.75/MWh
and the average real-time LMP was U.S.$ 32.38. Therefore the
average day-ahead LMP value was 1.1% higher than the average real-time LMP value. The relationship between the average Day-ahead LMP and the average real-time LMP varies by
hour of the day. A plot of the PJM average hourly system LMP
is shown in Fig. 1 [1].
The plot, Fig. 1, illustrates the close relationship that has developed between day-ahead and real-time prices. The fundamental incentives mentioned previously drive this convergence,
but the convergence also occurred quickly because of the flexibility provided by the virtual bidding rules. The PJM day-ahead
design makes it easy to submit virtual supply offers and demand
bids which promotes liquidity and a robust market. During the
year 2001, the average hourly amount of virtual supply offers
cleared in the day-ahead market was 6547 MW [1]. The onpeak
hour average was 8094 MW and, at times, the cleared virtual
supply offers cleared were over 18 000 MW. The average hourly
amount of virtual demand bids cleared in the Day-ahead market
was 5393 MW [1]. The on-peak hour average was 6298 MW
and, at times, the cleared virtual supply offers cleared were over
16 000 MW. These results demonstrate the high degree of liquidity in the day-ahead and forward markets.
III. REAL-TIME ENERGY MARKET
The PJM real-time energy market is based on actual real-time
operating conditions. Real-time LMPs are calculated based on
the actual system operating conditions as described by the PJM
OTT: EXPERIENCE WITH PJM MARKET OPERATION, SYSTEM DESIGN, AND IMPLEMENTATION
state estimator using the applicable generation offer data and
dispatchable external transactions. Generators that are available
but not selected in the day-ahead scheduling may alter their bids
for use in the real-time energy market during the generation rebidding period from 4:00 to 6:00 P.M. (otherwise their original
day-ahead market bids remain in effect for the real-time energy
market). LSEs will pay real-time LMPs for any demand that
exceeds their day-ahead scheduled quantities (and will receive
revenue for demand deviations below their scheduled quantities). Generators are paid real-time LMPs for any generation that
exceeds their day-ahead scheduled quantities (and will pay for
generation deviations below their scheduled quantities). Transmission customers pay congestion charges based on real-time
LMPs for bilateral transaction quantity deviations from dayahead schedules. All spot purchases and sales in the balancing
market are settled at the real-time LMPs.
A. Overview of Real-Time LMP Calculation
At 5-min intervals, locational marginal prices (LMPs) are calculated for all PJM load busses and generation busses that are
modeled in the PJM state estimator. LMPs are also calculated
for PJM interface busses with other control areas and for other
busses outside the PJM control area as required.
In order to perform LMP calculations and to perform the associated energy settlements and billing, a complete set of input
data are required. This set of input data includes
• accurate model of the actual operating conditions that exist
on the PJM power grid;
• complete description of all external transactions;
• full set of offer data from generating resources;
• set of dispatchable transactions;
• list of binding transmission constraints;
• economic dispatch instructions;
• log of dispatching instructions.
The PJM state estimator provides the initial powerflow solution that is required as input to the LMP calculation.
All PJM generation that is following PJM dispatch instructions are eligible to set LMP values. In addition to generation,
external transactions that are designated as dispatchable and are
following PJM dispatch instructions are eligible to set LMP
values. Since the LMP model includes a detailed model of adjacent external systems, loop flow effects are implicitly included
in the calculations.
In the real-time energy market, PJM dispatchers meet
the energy demand while respecting transmission security
constraint using the least-cost security constrained economic
dispatch program, the unit dispatch system (UDS). The UDS
is an ex-ante dispatch that is based on the projected system
conditions within the next 5 min. The LMP calculations are
ex-post and are based on the actual generation response to
the ex-ante dispatch that was sent 5 min before. Since the
LMP calculation is based upon the actual operating conditions
existing in the PJM control area as described by the PJM state
estimator solution, the LMP values are calculated based on a
dynamic model of the PJM power grid. The LMP calculation
will take into account the current transmission and generation
outages as well as transmission limitations that are identified
531
by the PJM dispatchers when the PJM control area is operating
out of economic merit to control such limitations.
B. LMP Data Model Input
1) Offer Data From Generating Resources: Offer data from
generating resources are stored in the markets database with all
offer data locked as of noon the day before the actual operating
day. These data along with demand bids, and external transactions are used in the PJM day-ahead market to determine the
actual day-ahead scheduled quantities, day-ahead LMP values
and net tie schedules. If a generator offer is accepted in the
day-ahead market, then the offer carries over into the real-time
market, otherwise the generator may changes its offer data for
the Real-time market during the re-bid period (4:00–6:00 P.M.).
After the re-bid period, a reserve adequacy assessment is performed by PJM to determine if additional steam units, above
those scheduled in the day-ahead market results, need to be
scheduled in advance of the operating day.
During the operating day, the PJM dispatch will communicate desired dispatch levels by sending economic price signals
(or economic dispatch rates) and/or individual unit megawatt to
the generators. Generators that are following economic dispatch
instructions will achieve the desired megawatt output level that
is described in the dispatch signal by comparing the dispatch
rate it receives from PJM to its offer curve.
2) Transaction Data: Transaction schedules can be
submitted for the day-ahead energy market, day-ahead
prescheduling for the real-time energy market or hour by hour
into the real-time energy market during the operating day. All
transaction schedules crossing the PJM control area boundary
must be entered into the PJM energy management system for
creation of pool-to-pool schedules and must include designation
of a point of receipt and point of delivery. Points of import into
the PJM control area are chosen from a set of external interface
points into the PJM control area. Points of export from the PJM
control area are also chosen from the set of external interface
points. Points of receipt or delivery by a participant within the
PJM control area will be chosen from the list of valid sources
and sinks listed on the PJM OASIS. Dispatchable transactions
into the PJM control area that are following economic dispatch
instructions are eligible to participate in the calculation of
LMPs and are modeled as generation (or load) at the designated
point of receipt (or delivery).
3) Binding Transmission Constraints: When the PJM EMS
system detects possible upcoming transmission limit violations,
the PJM dispatch investigates solutions to the problem. If the
transmission limitation can be resolved through system reconfiguration (PAR operation or switching) then the constraint is
managed using the EMS system. If the transmission violation
requires redispatch, the system operator transfers the transmission constraint information to the unit dispatch system for resolution. If the transmission constraint becomes a binding constraint in the security-constrained economic dispatch solution,
the unit dispatch system will transfer the binding constraint information to the locational price calculation module. The LPA
contingency processor translates this information and inputs the
transmission constraint to the LPA. The three types of transmission constraints that can be modeled in the LPA are detailed.
532
1) Reactive interface limits
Voltage and stability limits that are caused by regional
transfers are modeled as interface limits. Interface limits
are modeled in PJM system operations, and therefore in the
LPA, as a limitation to the total flow on a set of transmission lines. The PJM reactive interfaces describe key transmission boundaries on the PJM transmission system that
measures the voltage performance of specific areas of the
power grid.7
2) Thermal limits without contingency
These are limits to the amount of power that can flow on a
single transmission line due to physical limitations such as
conductor heating, line sag, etc. These limits are modeled
in the LPA such that the flow on the line is held at or below
the state estimator value.
3) Contingency limits
These limits are thermal limits that anticipate the loss of
another transmission facility. A contingency limit is evaluated by calculating the resulting flow on the monitored
facility for the loss of the another transmission facility (the
contingency facility) or set of transmission facilities. This
resulting flow is called the contingency flow. These limits
are modeled in the LPA such that the contingency flow is
held at or below the contingency flow that is calculated
based on the state estimator solution.
C. Description of the PJM LMP Model
The PJM LMP calculation process consists of a variety of
programming modules that are executed as part of the real-time
sequence that executes every five minutes on the PJM energy
management system (EMS). A functional diagram of the PJM
LMP model is shown in Fig. 2. As indicated in Fig. 2, the main
modules of the PJM LMP model are
• state estimator;
• LPA preprocessor;
• locational price algorithm (LPA);
• unit dispatch system (UDS).
Each of these modules is described in detail below. In addition
to the main modules that are listed in the diagram, several other
programs designed to ensure data integrity are executed as part
of the PJM LMP calculation process. These programs include
the LPA Input Data Consistency Check (ICC) program and the
LPA output data consistency check (OCC) program.
The primary purpose of the ICC is to perform data verification
on all input data to the LMP calculation process to ensure that
the information is current, consistent and reasonable. The ICC
program will monitor all input data files to ensure that each file’s
operating system timestamp and internal timestamps are current
and consistent with the interval being processed. In addition, the
ICC will check any transmission constraint data to verify that
any contingencies entered and their corresponding controlling
actions are all entered consistently, accurately, and in a timely
manner. The ICC also monitors the status of the state estimator
solution to ensure that the solution is a valid solved powerflow
7Interface limits are modeled in the LPA such that the sum of the flow on the
interface will beheld at the megawatt value of the interface flow from the state
estimator solution or lower.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
Fig. 2.
Functional diagram of PJM LMP model.
solution. The ICC executes at the beginning of the LMP calculation sequence and if a problem is identified the program logs
the error to the LPA error log and produces an appropriate alarm
to the system operator.
The primary purpose of the OCC is to verify that the LMP
calculation is performed accurately and completely. The OCC
will check all the output data files to ensure that each program
completed successfully and produced its corresponding output
file along with several checks of the results for reasonability.
The OCC will check the file’s operating system timestamp and
any internal timestamps to ensure the file’s times are current
and consistent with the interval being processed. In addition,
the OCC will check the resultant LMP’s for consistency with
any constraint information. This program performs LMP validation by verifying that the LMP of each generator that is a
control variable in the LPA is consistent with the price bounds
that are set by the generators offer data and dispatch rate. The
OCC executes at the end of the LMP calculation sequence and
if a problem is identified the program logs the error to the LPA
error log and produces an appropriate alarm to the system operator.
1) PJM State Estimator: The LMP calculation depends
upon having a complete and coherent power flow solution
as input. This input requirement can be achieved by using a
state estimator. The state estimator is a standard power system
operations tool whose purpose is to provide a base case power
flow solution for input into other computer programs. The state
estimator uses actual operating conditions that exist on the
power grid (as described by metered inputs) along with the
fundamental power system equations to calculate the remaining
flows and conditions that are not metered. Since the state
estimator solution provides a complete and coherent model of
actual operating conditions based upon observable (metered)
input and an underlying mathematical model, it can be used
to provide the basis for the LMP calculations. The inputs to
the state estimator are the available (metered) real-time measurements, the current status of equipment (lines, generators,
transformers, etc.), and the bus load distribution factors.
This standard industry tool depends upon data redundancy
and the underlying physical and mathematical relationships of
the power system to provide a solution with less error than the
OTT: EXPERIENCE WITH PJM MARKET OPERATION, SYSTEM DESIGN, AND IMPLEMENTATION
original measurements. Therefore the state estimator can correct
“bad data” and calculate missing data in the model to provide a
coherent representation of existing network conditions.
The PJM state estimator is run on a one minute cycle and can
provide the following inputs to the LMP module
•
•
•
•
•
•
ac powerflow solution;
actual generator megawatt output;
bus loads;
tie line flows;
megawatt losses by transmission zone;
actual megwatt flow on any constrained transmission facility.
2) LPA Preprocessor: Since the LMP calculation is based
on actual generation output rather than a theoretical optimal dispatch, it is necessary to screen generators and transactions to determine if they are eligible to participate in the LMP calculation.
The LPA preprocessor performs this screening function by
analyzing the following to determine if a generator is following
economic dispatch requests.
•
•
•
•
generator state estimated megawatt hour output;
generator offer price curves;
economic dispatch rates;
desired megawatt level for each generator that was specified by UDS.
The program therefore acts as a real-time performance
monitoring function for generators that have designated themselves as dispatchable. Dispatchable generators whose actual
megawatt output is 110% or less than the desired megawatt
level are considered to be following the economic dispatch instructions and are therefore eligible to be passed through to the
LMP calculation as flexible generators. The LPA preprocessor
also identifies and validates any generators that are specifically
requested by the UDS program to operate out of economic
merit order in order to control a transmission constraint.
These generators are designated as eligible to set LMP if they
are on-line and following the dispatch instruction. The LPA
preprocessor also screens transactions that are designated as
dispatchable to determine if their offer data are consistent with
current dispatch rates and if they are therefore eligible to set
LMP. Generators that are not eligible to participate in LMP
calculations are those that are declared must run or that are
not following economic dispatch requests based on the criteria
outline before.
Generators and transactions that are eligible to participate in
the LMP calculation are those that are following the economic
dispatch requests as described before. These eligible generators or transactions are modeled in the LMP calculation as flexible generators with offer prices that correspond to the value
from their offer curve at actual megawatt output (or megawatt
schedule for transactions). The LPA preprocessor calculates this
real-time offer value using the following criteria
• if the generator’s state estimated megawatt value is less
than or equal to the desired megawatt value, then the
real-time offer value is calculated by comparing the state
estimated megawatt output to the offer curve.
• if the generator’s state estimated megawatt value is greater
than the desired megawatt value, then the real-time offer
533
value is calculated by comparing the desired megawatt
value to the offer curve.
The eligible generators and transactions are introduced to the
LPA (LPA) as flexible generators (or loads) and are modeled
at actual megawatt output with a small bandwidth to allow for
solution tolerance. Generators that are not eligible to participate
in LMP calculations are modeled as inflexible generators with
their megawatt output fixed at the actual megawatt value from
the state estimator solution.
3) Locational Price Algorithm: The function of the LPA
(LPA) is to determine the LMP values for each of the PJM nodes
in the state estimator model and for interface busses to the PJM
and PJM control areas on a 5-min basis. The LMP are defined
as the cost to serve the next increment of load at each node bus
location for the current system state estimated operating point
and taking into account flexible generator Real-time bid prices
and the buses’ location with respect to transmission limitations.
Given the input from the state estimator and the set of flexible
generators with bid prices at their actual operating points, the
calculation of LMP is relatively straight forward. The LMPrice
calculation is an incremental linear optimization problem that
is formulated at the current state estimated operating point.
The objective is to minimize the cost function subject to
the power balance constraint, generation megawatt bounds,
transaction megawatt bounds and any transmission constraints
that currently exist on the system.
Since the goal of the PJM LMP system is to calculate the
real-time LMP values based on actual system operating conditions, the state estimated powerflow solution is used as a starting
point for the incremental linear programming formulation. This
powerflow solution is then linearized in order to perform the
LMP calculations. As outlined in previous sections, the set of
flexible generators and transactions is determined by the LPA
preprocessor and is input to the LPA as a set of control variables.
and the
The set of flexible generators and sale transactions
are modeled in the forset of flexible purchase transactions
mulation at the state estimated megawatt amount with a small
bandwidth to allow for solution tolerance. The cost coefficients
in the objective function for the flexible generators and transactions are set equal to the real-time bid that is calculated by the
LPA preprocessor based on the state estimated megawatt level
and the incremental offer (or bid) curve. These cost coefficients
are assumed to have a constant slope.
The PJM incremental linear programming formulation is as
follows
Minimize
subject to
534
where
change in power output for generator ;
upper megawatt bound for generator ;
lower megawatt bound for generator ;
calculated real-time offer for generator ;
calculated real-time bid for load (transaction) ;
change in power consumption for load (note: in
practice the only dispatchable loads that currently
exit are external purchase transactions);
upper megawatt bound for load ;
lower megawatt bound for load ;
matrix of shift factors for generation bus (with respect to the reference bus) on the binding transmission constraints ( );
matrix of shift factors for load bus (with respect
to the reference bus) on the binding transmission
constraints ( ).
The shift factor matrices referenced above represent a
set of shift factors based on the system topology described
by the binding transmission constraint. For interface limits
and thermal limits w/o contingency, the transmission system
configuration used to calculate the shift factors is based on
the current topology as described by the state estimator. For
contingency limits, the state estimator topology is modified to
include the removal of the contingent transmission facilities
for the shift factor calculation. Shift factors for a transmission
constraint are a measure of the change in power flow on the
constraint’s monitored element for a unit change in megawatt
injection at a bus and a corresponding unit change in megawatt
withdrawal at the reference bus.
The LMP values at each bus are by-products of the linear programming formulation that is listed before. The LMP value at
a particular location is essentially the sum of the marginal price
of generation at the reference bus plus the marginal congestion
price at the location associated with the various binding transmission constraints. The marginal prices associated with various constraints in the optimization problem are called shadow
prices. The shadow price of a constraint can be explained as the
incremental change in value of the objective function for a unit
change in the limit (right hand side) of the constraint. Therefore, an equation for computing LMP values can be expressed
in terms of these shadow prices.
The LMP equation can be written as follows:8
where
LMPrice at bus ;
marginal price of generation at the reference bus;
shift factor for bus on binding constraint ;
shadow price of constraint .
It should be noted that the cost of marginal losses in the PJM
LMP program is set to zero; therefore, the marginal loss term
does not appear in the above equation.
4) Unit Dispatch System: The UDS is a software tool that
is designed to provide the PJM dispatchers with the capability
to manage changes in load, generation, interchange, and trans8The current PJM model does not reflect the cost of marginal losses in either
the dispatch instructions or in the LMP values.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003
mission constraints simultaneously on a near real time basis,
by providing a recommended dispatch solution. This solution
looks at current system conditions, forecasted load, generation,
and transactions to produce dispatch solutions for a user-selected look-ahead time. This allows the operator to simultaneously manage multiple transmission constraints.
The UDS is not a stand-alone system. It is an application that
processes data from the markets database and other PJM systems. Other data sources include
• load forecast data from EMS (GDC servers);
• ACE, steam deviation, regulation signal from EMS (COM
servers);
• constraint data-unit sensitivities from EMS (NA servers);
• state estimator output from EMS (NA servers);
• outage data from eDART;
• transaction data from EES.
The UDS executes a dispatch solution automatically every 5
min or when executed by the operator. To calculate the solution, UDS looks at online and available generation, generator
bid data, forecasted load, scheduled and current interchange,
area control error (ACE), and the regulation signal. The application then produces three cases with each solution. Each of these
solution cases contains
• recommended set of zonal dispatch rates;
• list of exceptions to the dispatch rates for constraint control;
• individual unit dispatch rates;
• desired megawatt level for each generator.
UDS gathers transmission constraint information from the
EMS alleviate overload and develops its dispatch solution based
on using the most economic generators to control a given constraint. The optimization that takes place when the UDS executes will ensure that no generator is moved to alleviate one
constraint, only to aggravate another constraint.
When the operator approves a recommended solution, the
zonal dispatch rates and/or individual unit megawatt are bridged
to the EMS, where they are automatically sent out to generators
or local control centers. Units that appear on the UDS’ exception list must be manually dispatched.
In addition to being used for economic dispatch, results of
each recommended solution are used as input to the locational
price calculation process. When the operator approves a recommended solution, dispatch rates and desired megawatt level for
each generator is sent to the LPA preprocessor. UDS also produces a list on binding constraints that are sent to the LPA.
REFERENCES
[1] PJM 2001 State of the Market Rep., Norristown, PA, June 2002.
Andrew L. Ott received the B.S. degree in electrical engineering from Penn
State University, University Park, and the M.S. degree in applied statistics from
Villanova University, Villanova, PA.
Currently, he is responsible for the oversight of PJM market development,
PJM market operations, and PJM market settlements. He joined PJM, Norristown, PA, in October 1996. He was responsible for implementation of the current PJM locational marginal pricing system, the PJM financial transmission
rights auction, and the PJM day-ahead energy market. Prior to joining PJM, he
was with GPU for 13 years in transmission planning and operations.